Question

the surface area of this cone is 392.5 square feet. what is the slant height of this cone? round your answer to the nearest hundredth. 5 ft s ≈ feet

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cone is $A=\pi r(r + l)$, where $A$ is the surface area, $r$ is the radius, and $l$ is the slant height. Given $A = 392.5$ square feet and $r = 5$ feet.

Step2: Substitute values into formula

Substitute $A = 392.5$ and $r = 5$ into $A=\pi r(r + l)$:
$392.5=\pi\times5\times(5 + l)$
First, calculate $\pi\times5 = 5\pi\approx5\times3.14 = 15.7$.
The equation becomes $392.5=15.7\times(5 + l)$.

Step3: Solve for $l$

Divide both sides of the equation by $15.7$:
$\frac{392.5}{15.7}=5 + l$
$25=5 + l$.
Subtract 5 from both sides:
$l=25 - 5=20$

Answer:

$20.00$